The synthesis of sequential machines by interconnections of copies of a fixed module is considered. A family of modules M<inf>r,p</inf>for positive integers r and p, is defined. Mr,p can be used to synthesize sequential machines with 2<sup>P</sup>input symbols. A nondeterministic sequential machine (NSM) is said to be r-bounded if it has one initial state and for no state and input are there more